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In this paper, we focus on dynamics in a basic discrete-time system of host–parasitoid interaction. We perform local stability analysis of this system. Furthermore, both flip and Neimark–Sacker bifurcations are also analyzed in the interior of $R_{ +}^{2}$ by using center manifold theorem and bifurcation theory. Finally, numerical simulations are deployed to validate our results with theoretical analysis and to exhibit the dynamical behaviors.

Dynamic complexity and bifurcation analysis of a host–parasitoid model with Allee effect and Holling type III functional response